Some of the trips clearly qualify as "official business," such as those to the economic summit meeting of Western government leaders last month in Venice and the memorial service for the late Japanese Prime Minister Masayoshi Ohira earlier this month in Tokyo.

Others are designated "nonpolitical," but carry strong political overtoneS. Often, there's a fine line to be drawn. For example:

Mr. Carter's visit in June to National Urban League president Vernon E. Jordan Jr. At his hospital room in Fort Wayne, Ind., came just two days before crucial presidential primary elections in several states with large black electorates.

And his swoop last week into Detroit to announce federal relief for the ailing auto industry momentarily upstaged Republicans gathering there for their national convention.

A third group of Carter trips is a potpourri of presidential business and politicking.

On his excursion earlier this month to California and Florida, for example, the "nonpolitical" President addressed the National Education Association and the National Association for the Advancement of Colored People (slipping in veiled warnings about his unnamed Republican opponent). Meanwhile, the President, as party leader, raised $500,000 for the Democratic National Committee at a round of dinners, brunches, and receptions for the party faithful.

Air travel -- expensive enough for any ordinary, economy-fare tourist -- is super-expensive for the President and his entourage.

The bills for the past two months' trips are still trickling in, and have yet to be tallied. But air transportation alone -- aboard Air Force One, the President's converted 707 jetliner which costs $4,530 per hour to operate -- is perhaps the largest single expense. It will amount to some $362,400.

When Mr. Carter travels on business deemed at least nominally official, the American taxpayers pick up the tab. When political activities are involved, Democrats share the costs.

On the trip that combines government business and political stumping, for instance, the bills for the former are paid by the US Treasury and those for the latter are sent to the Democratic National Committee, the Carter-Mondale reelection campaign, or the local Democratic Party organization.

Passengers aboard Air Force One in a political capacity are billed for the equivalent first-class commercial air fare plus $1.

Any remaining costs not easily identifiable as either political or nonpolitical are then divided up in proportion to the approximate time spent on each (two-thirds political and one-third nonpolitical, for example).

Despite such painstaking accounting, however, the net financial impact of the formula is stirring controversy.

Are American taxpayers subsidizing Mr. Carter's recent campaign swings -- or, depending on one's point of view, are the Democrats helping to underwrite the cost of his official travels?

Either interpretation is possible. The sharing of common costs spares either the taxpayers or the Democrats from footing the entire bill for flying the PResident somewhere just to deliver a presidential speech or just to appear at a party fund-raiser.